238 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



can there ever be much use in such observations unless the amount 

 of pressure can be put into the mathematical theory. The so- 

 called mechanical theory is thus not mechanical in any sense ; it 

 is based on pressures which cannot be measured, or even proved 

 to exist, and may therefore be wholly imaginary, and such theories 

 are as useless as any other standpoint to which the stigma of 

 " Nature Philosophy " may be attached.* 



In considering the special standpoint taken up by Schwendener, 

 and the importance attributed by him to displacements, it must be 

 remembered that Schwendener formulated the Dachstuhl theory 

 to explain the well-known observation that the general facts of 

 phyllotaxis phenomena as seen in growing shoots did not agree 

 with the postulated accurate angular divergences of the Bonnet- 

 Schimper helical system : and also that the most important piece 

 of obvious evidence of such alteration was afforded by the very 

 general displacement of the angles of primordia which become 

 angular under mutual pressure. This latter feature may be con- 

 sidered separately ; at present it is only essential to point out 

 that displacement of angles does not necessarily imply displace- 

 ment of the whole member, and that, the Schimper-Braun Archi- 

 medean formulae having been shown to be fundamentally incorrect 

 for developing systems, — the error of the construction being 

 rendered clear by the log. spiral theory, — the correction of such 

 constructions by hypothetical secondary displacement becomes 

 wholly unnecessary. 



Schwendener's theory, put forward in 1875, has long held the 

 field, since from the complexity of its assumptions its application 

 to the plant was not easy to understand and still more difficult 

 to disprove. The conception of what has been termed " bulk- 

 ratio" was introduced as a factor in determining phenomena of 

 spiral phyllotaxis ; but as previously shown, however valuable 

 such a convention may be, it affords no clue whatever to the still 

 more fundamental phenomena of asymmetry and the true sym- 

 metry of whorled construction {cf. Part II.). 



Schwendener also assumed as facts of observation certain dis- 

 placements of the lateral members, and close lateral contact 

 * Of. Weisse, Pringsheim's Jahrb., vol. xxxix. p. 419. 



